thermodynamics - Why is entropy an extensive quantity?

If we have two identical isolated macroscopic systems both with energy $E$. The number of accessible states of each of them is $\Omega(E)$ and hence the entropy is $\ln\Omega(E)$. Now if we put them in thermal contact to form a larger isolated system with energy 2$E$ (suppose there are weakly interacting). Then the number of accessible states of the whole system is

$$\sum_x\Omega(x)\Omega(2E-x)$$ but not just $$\Omega(E)\Omega(E)$$

So the total entropy is $$\ln\sum_x\Omega(x)\Omega(2E-x)$$

But not just $$\ln[\Omega(E)\Omega(E)]=\ln\Omega(E)+\ln\Omega(E)=S_1+S_2$$.

So why do we say entropy is extensive?